Fourth Order Gravity, Scalar-Tensor-Vector Gravity, and Galaxy Rotation Curves

Abstract

The Lambda-CDM model is the best fit to cosmological data, and to the observed galactic rotation curves. However, in the absence of a direct detection of dark matter one should explore theories such as MOND, and perhaps also modified gravity theories like fourth order gravity and Scalar-Tensor-Vector Gravity [STVG] as possible explanations for the non-Keplerian behaviour of galaxy rotation curves. STVG has a modified law for gravitational acceleration which attempts to fit data by fixing two free parameters. We show that, remarkably, the biharmonic equation which we get in the weak field limit of the field equations in a fourth order gravity theory implies a modification of Newtonian acceleration which is precisely of the same repulsive Yukawa form as in the STVG theory, and the corrections could in principle be large enough to try and explain the observed rotation curves. We also explain how our model provides a first principles understanding of MOND. We also show that STVG and fourth order gravity predict an acceleration parameter $a_0$ whose value is of the same order as in MOND.

13 pages, 3 figures, major revision including change in title and conclusions, accepted for publication in Phys. Rev. D

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Cited by in corpus (8)

• Casimir Wormholes
• Particle Dynamics Near Kerr-MOG Black Hole
• Constraints on Modified Gravity Models from White Dwarfs
• Astrophysical Gravitational Waves in Conformal Gravity
• Exact cosmological black hole solutions in Scalar Tensor Vector Gravity
• Cosmic Acceleration in a Model of Fourth Order Gravity
• Constraints on fourth order gravity from binary pulsar and gravitational waves
• Yukawa-Casimir Wormholes